Güttel, Stefan and Schweitzer, Marcel (2020) A comparison of limited-memory Krylov methods for Stieltjes functions of Hermitian matrices. [MIMS Preprint]
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Abstract
Given a limited amount of memory and a target accuracy, we propose and compare several polynomial Krylov methods for the approximation of f(A)b, the action of a Stieltjes matrix function of a large Hermitian matrix on a vector. Using new error bounds and estimates, as well as existing results, we derive predictions of the practical performance of the methods, and rank them accordingly. As by-products, we derive new results on inexact Krylov iterations for matrix functions in order to allow for a fair comparison of rational Krylov methods with polynomial inner solves.
| Item Type: | MIMS Preprint |
|---|---|
| Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis |
| Depositing User: | Stefan Güttel |
| Date Deposited: | 11 Jun 2020 23:23 |
| Last Modified: | 11 Jun 2020 23:23 |
| URI: | https://eprints.maths.manchester.ac.uk/id/eprint/2769 |
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